A parametric family of quintic Thue equations

نویسندگان

  • István Gaál
  • Günter Lettl
چکیده

For an integral parameter t ∈ Z we investigate the family of Thue equations F (x, y) = x + (t− 1)xy − (2t + 4t + 4)xy + (t + t + 2t + 4t − 3)xy + (t + t + 5t+ 3)xy + y = ±1 , originating from Emma Lehmer’s family of quintic fields, and show that for |t| ≥ 3.28 ·1015 the only solutions are the trivial ones with x = 0 or y = 0. Our arguments contain some new ideas in comparison with the standard methods for Thue families, which gives this family a special interest.

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عنوان ژورنال:
  • Math. Comput.

دوره 69  شماره 

صفحات  -

تاریخ انتشار 2000